Random variables X and Y have joint density:

f_x,y(x,y) = c(y^(2)-x^(2))e^(-y) when -y<x<y, y>0

f_x,y(x,y) = 0 otherwise

Here, c is a constant.

I have shown that Y has a gamma density, and have found that c=1/8.

Now, how do I find the density of Y^(3)?

Any help is greatly appreciated! Thanks in advance.